Answer:
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
In this case, we want to prepare a buffer solution with pH 5, using acetic acid and sodium acetate. The acid in this case is acetic acid, and the conjugate base is acetate. The acid dissociation constant (Ka) of acetic acid is given as 1.8×10^-5.
Let x be the concentration of sodium acetate and y be the concentration of acetic acid in moles per liter. Then, we can write:
pH = pKa + log([A-]/[HA])
5 = 4.74 + log(x/y)
Simplifying, we get:
log(x/y) = 0.26
Taking antilog on both sides, we get:
x/y = antilog(0.26)
x/y = 1.8
Therefore, the ratio of sodium acetate to acetic acid that must be used to prepare a buffer solution of pH 5 is 1.8:1.